cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A238107 5!*a(n) = number of self-avoiding paths in the 5-cube from 00000 to 11111 and having length 5 + 2*n.

Original entry on oeis.org

1, 10, 107, 1097, 9754, 72305, 448536, 2243671, 8631118, 24044702, 44617008, 48280086, 24000420, 3080792
Offset: 0

Views

Author

N. J. A. Sloane, Mar 01 2014

Keywords

Comments

5!*a(n) counts paths with n back-steps.

Links

Crossrefs

Cf. A059783, A238108.

A238108 a(n) = (n - 1)*(n - 2)*(5*n^4 + 3*n^3 + 34*n^2 - 264*n + 180)/360.

Original entry on oeis.org

1, 0, 0, 1, 19, 107, 386, 1086, 2597, 5530, 10788, 19647, 33847, 55693, 88166, 135044, 201033, 291908, 414664, 577677, 790875, 1065919, 1416394, 1858010, 2408813, 3089406, 3923180, 4936555, 6159231, 7624449, 9369262
Offset: 0

Views

Author

N. J. A. Sloane, Mar 01 2014

Keywords

Comments

n!*a(n) = number of self-avoiding paths in n-cube from 00...0 to 11...1 with two back-steps.

Links

Crossrefs

Cf. A059783, A238107.

Programs

  • Mathematica
    Table[(n-1)(n-2)(5n^4+3n^3+34n^2-264n+180)/360,{n,0,40}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,0,0,1,19,107,386},40] (* Harvey P. Dale, Mar 15 2015 *)

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=19, a(5)=107, a(6)=386, a(n)= 7*a(n-1)- 21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Mar 15 2015
G.f.: ( -1+34*x^3-47*x^4+26*x^5-8*x^6+7*x-21*x^2 ) / (x-1)^7 . - R. J. Mathar, Apr 23 2015

A215577 Number of nonintersecting (or self-avoiding) rook paths joining opposite corner cells of an n X n X n grid, avoiding cells that are not on the surface.

Original entry on oeis.org

1, 18, 340812, 1553113040
Offset: 1

Views

Author

Alex Ratushnyak, Aug 16 2012

Keywords

Comments

When n<3 there are n^3 cells available, otherwise n^3 - (n-2)^3.
The length of the step is 1. The length of the path varies.

Crossrefs

Cf. A007764, A059783.

Programs

  • C
    #include     // GCC -O3
char grid[4][4][4];
long long SIZE;
long long calc_ways(long long x, long long y, long long z) {
    long long n;
    if (grid[x][y][z]) return 0;
    if (x+y+z==SIZE*3-3) return 1;
    grid[x][y][z]=1;
    n=0;
    if (x>0)        n =calc_ways(x-1,y,z);  // go left
    if (x0)        n+=calc_ways(x,y-1,z);  // down
    if (y0)        n+=calc_ways(x,y,z-1);  // level down
    if (z
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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